69 lines
2.0 KiB
Python
69 lines
2.0 KiB
Python
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# Copyright (C) 2015 by
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# Alessandro Luongo
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# BSD license.
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#
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# Authors:
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# Alessandro Luongo <alessandro.luongo@studenti.unimi.it>
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#
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"""Functions for computing the harmonic centrality of a graph."""
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from functools import partial
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import networkx as nx
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__all__ = ['harmonic_centrality']
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def harmonic_centrality(G, nbunch=None, distance=None):
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r"""Compute harmonic centrality for nodes.
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Harmonic centrality [1]_ of a node `u` is the sum of the reciprocal
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of the shortest path distances from all other nodes to `u`
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.. math::
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C(u) = \sum_{v \neq u} \frac{1}{d(v, u)}
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where `d(v, u)` is the shortest-path distance between `v` and `u`.
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Notice that higher values indicate higher centrality.
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Parameters
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----------
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G : graph
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A NetworkX graph
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nbunch : container
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Container of nodes. If provided harmonic centrality will be computed
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only over the nodes in nbunch.
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distance : edge attribute key, optional (default=None)
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Use the specified edge attribute as the edge distance in shortest
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path calculations. If `None`, then each edge will have distance equal to 1.
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Returns
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-------
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nodes : dictionary
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Dictionary of nodes with harmonic centrality as the value.
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See Also
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--------
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betweenness_centrality, load_centrality, eigenvector_centrality,
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degree_centrality, closeness_centrality
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Notes
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-----
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If the 'distance' keyword is set to an edge attribute key then the
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shortest-path length will be computed using Dijkstra's algorithm with
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that edge attribute as the edge weight.
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References
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----------
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.. [1] Boldi, Paolo, and Sebastiano Vigna. "Axioms for centrality."
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Internet Mathematics 10.3-4 (2014): 222-262.
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"""
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if G.is_directed():
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G = G.reverse()
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spl = partial(nx.shortest_path_length, G, weight=distance)
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return {u: sum(1 / d if d > 0 else 0 for v, d in spl(source=u).items())
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for u in G.nbunch_iter(nbunch)}
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